Condorcet Jury Theorem (1785)

• The Condorcet Jury Theorem states that if each member of a jury has a probability greater than 1/2 of making the correct decision, then as the number of jurors increases, the probability that the majority decision is correct approaches 1.

\[ P(\text{majority correct}) \to 1 \text{ as } n \to \infty \\ \iff \text{independence of errors} \]

Boosting Weak Learners (1988)

Model Stacking (1992)

Ensemble Methods Summary

Stacking into Boosting

• Why not both?

cv = StratifiedKFold(n_splits=5, shuffle=True, random_state=42)

lin = Pipeline([
  ("scaler", StandardScaler()),
  ("lr", LogisticRegression(max_iter=1000))
])

stack = StackingClassifier(estimators=[("lin", lin)],
  final_estimator=LGBMClassifier(),
  stack_method="predict_proba", passthrough=True, cv=cv
)

stack.fit(X_train, y_train)
y_pred = stack.predict(X_test)

The Dunbar Number (1992)

Dunbar cont’d: How Hedge Funds Manage It

The Common Task Framework (2007-)

Common Task Framework (cont’d)

• “The Kaggle Grandmasters Playbook: 7 Battle-Tested Modeling Techniques for Tabular Data”, September 18, 2025, Nvidia Blog, link.

Machine, Platform, Crowd (2017)

Theory Takeaways

Quant Equity Workflow

• Larkin, Jonathan R., “A Professional Quant Equity Workflow”, Quantopian Blog, 2016, link.
• Separate teams are focused along an assembly line
  • Data acquisition
  • Alpha research (aka feature engineering)
  • Signal combination (aka modeling)
  • Risk and transaction cost modeling
  • Portfolio construction (aka optimization)
  • Execution

Quant Equity Workflow

Quant Equity Workflow

flowchart LR

    DATA(Data) --> UDEF(Universe Definition)

    UDEF --> A1(alpha 1)
    UDEF --> A2(alpha 2)
    UDEF --> ADOTS(alpha...)
    UDEF --> AN(alpha N)

    A1 --> ACOMBO(Alpha Combination)
    A2 --> ACOMBO
    ADOTS --> ACOMBO
    AN --> ACOMBO

    DATA --> TARGET(Target)
    TARGET --> ACOMBO
    TARGET --> PCON
    DATA --> RISK(Risk & T-Cost Models)

    ACOMBO --> PCON(Optimization)
    RISK --> PCON

    PROD{{t-1 Portfolio}} --> PCON
    PCON --> IDEAL{{Ideal Portfolio}}
    IDEAL --> EXEC
    
    EXEC(Execution)

Workflow: Minimal Non-Trivial Implementation

• Craft four simple alphas (momentum, reversal, quality, value)
• Create a target (forward 5d return demeaned)
• Combine alphas with linear model
• Use cvxportfolio machinery for risk model, t-cost model, optimization
• Cvxportfolio repo on github
• Boyd, Stephen, et al. “Multi‑Period Trading via Convex Optimization.” Foundations and Trends in Optimization, vol. 3, no. 1, 2017, pp. 1–76.

Introduction

• Traditional hedge funds: small teams, opaque processes, high fees
  
• New paradigm: decentralized hedge funds
  • Crowdsourced intelligence
    
  • Blockchain-based incentives
    
  • Global participation
    
• Case studies: Numerai, Yiedl, CrowdCent

Numerai – Overview

• San Francisco–based hedge fund (founded 2015)
  
• Crowdsources stock market predictions from global data scientists
  
• Uses a meta-model: ensemble of community models aggregated into live trading strategy
  
• Mission: “solve the hardest problem in finance” with diverse, anonymized datasets

Numerai – Community & Competitions

• Weekly data science tournaments
  
• Participants submit ML predictions on anonymized market data
  
• Scored on correlation with actual returns
  
• Staking with NMR tokens:
  • Stake NMR = confidence in predictions
    
  • Rewards for accuracy, penalties for errors

Numerai – Data & Roles

• Company: curates data, manages fund, constructs stake-weighted meta-model
  
• Community: builds models, submits predictions, stakes tokens
  
• Data: anonymized, obfuscated stock/market datasets
  
• Company executes trades; community generates intelligence

Numerai – Role of Crypto

• Numeraire (NMR): first hedge-fund-issued cryptocurrency
  
• Staking aligns incentives: accurate models gain rewards, inaccurate lose stake
  
• All payouts and stakes occur via Ethereum smart contracts
  
• Supports trustless, global participation

Yiedl – Overview

• Founded 2023, fully DAO-based hedge fund
  
• Mission: replace fund managers with blockchain data science tournaments
  
• Operates via on-chain vaults on Optimism + Synthetix
  
• Managed by token holders, not a centralized GP

Yiedl – Community & Competitions

• Weekly crypto-asset prediction tournaments
  
• Participants forecast asset returns, stake Yiedl tokens
  
• Predictions stored/encrypted on IPFS & blockchain
  
• Smart contracts auto-reward/penalize based on accuracy
  
• Two tracks:
  • Neutral vault: rank assets for market-neutral strategy
    
  • UpDown vault: propose portfolio weights

Yiedl – Data & Roles

• Data: curated decade-long crypto datasets (prices, on-chain metrics, sentiment)
  
• Community: builds predictive models, stakes tokens, governs DAO
  
• Company/DAO: develops infrastructure, aggregates predictions, executes trades via smart contracts
  
• Division: community = what to trade, DAO = how to implement

Yiedl – Role of Crypto

• YIEDL token:
  • Staking in competitions
    
  • Governance (DAO voting)
    
  • Rewards for accurate predictions
    
• All trades executed via DeFi protocols (Synthetix)
  
• On-chain fund = transparent, auditable, permissionless

CrowdCent – Overview

• Hybrid crowdsourced investment platform (2022–2023)
  
• Combines fundamental analysts + data scientists
  
• Mission: democratize asset management with human + machine intelligence
  
• “Next-generation of investing: decentralized, systematized, democratized”

CrowdCent – Community & Competitions

• Analysts: share investment theses (e.g. via SumZero)
  
• Data Scientists: join open ML challenges to evaluate ideas
  
• Examples:
  • Hyperliquid Challenge: rank crypto assets by 10–30d returns
    
  • Equity NLP Challenge: analyze analyst reports for predictive alpha
    
• Leaderboards, percentile scoring, meta-model aggregation

CrowdCent – Data & Roles

• Data:
  • Fundamental research from SumZero (analyst reports, ratings)
    
  • Market + crypto data, engineered features
    
• Community:
  • Analysts generate qualitative ideas
    
  • Data scientists build quantitative models
    
• Company: runs competitions, integrates data, manages portfolio construction & execution

CrowdCent – Role of Crypto

• No native token (as of 2025)
  
• Crypto as an asset class: community builds crypto strategies (Hyperliquid challenge)
  
• Integration with crypto projects:
  • Fund that stakes in Numerai’s NMR ecosystem
    
  • Bridges decentralized funds together
    
• Less “on-chain” than Yiedl, but embraces crypto markets and ethos

Conclusion

• Numerai: pioneered crypto-incentivized crowdsourced hedge fund
  
• Yiedl: DAO-based, on-chain hedge fund built entirely with DeFi
  
• CrowdCent: blends human fundamental research with ML and crypto strategies
  
• Common threads:
  • Community-driven intelligence
    
  • Machine learning aggregation
    
  • Cryptocurrency as incentive + infrastructure
    
• Future hedge funds: open, decentralized, global

Types of Collaboration

• Horizontal
• Vertical

Horizontal

• Human forecasts concatenated with machine forecasts
• Fit model on both

Vertical

• Stepwise: human first, machine second (or vice versa)

Motivation

• Canonical view: “Public” info is free and instantly priced (EMH).
• Reality: Converting public data → stock picks is costly (analysts, data prep, modeling, infra, time).
• Research question: How large are the economic costs of processing public information?

Study Design (High Level)

• Population: 3,337 active, diversified U.S. equity mutual funds (1990–2020).
• Build an AI analyst that uses only public data and realistic constraints.
• Compare:
  • Human manager (actual holdings)
  • AI-modified (hybrid; selective replacements)
  • AI-only (full replacement within style constraints)
• Measure: Dollar alpha and Sharpe; treat forgone gains as lower bound of managers’ marginal info-processing costs.

Key Findings (Punchline)

• AI-modified: +$17.1M incremental per quarter vs. human; ~93% of managers outperformed over their lifetimes.
• AI-only: +$17.2M incremental per quarter; ~42% allocated to style indices without hurting results.
• Sharpe improves materially (details ahead).
• Results robust to risk models, transaction costs, benchmark identification, and incentive heterogeneity.

Conceptual Framework

• Investors process info until marginal cost = marginal gain.
• If AI (public info only) can improve a manager’s portfolio under the manager’s constraints, the forgone gains represent a lower-bound on the manager’s marginal info costs.
• Human + machine is evaluated within fund style/risk/size/liquidity constraints.

Data Inputs (Public Only)

• Market (CRSP): prices, returns (incl. delisting), volatility, beta, liquidity/volume, market cap.
• Accounting (Compustat point-in-time; proper lags): profitability, accruals, leverage, growth, etc.
• Analysts (I/B/E/S): consensus EPS, recommendations, price targets (careful timing; summary files).
• Text (EDGAR): 10-K/Q and 8-K tone/complexity/uncertainty (point-in-time release).
• Macro (Welch–Goyal set): term/default spreads, D/P, E/P, etc.
• Ratings: S&P long-term issuer ratings.
• ~170 features; winsorization by feature type; point-in-time construction to avoid look-ahead.

Return Target & Benchmarking

• Predict quarter-ahead stock returns:
  • Preferred: DGTW benchmark-adjusted returns (size × B/M × momentum groups).
  • Also considered: excess returns vs. risk-free.
• Portfolio construction and evaluation are within DGTW groups to preserve style.

ML Pipeline (Pseudocode)

# =========================
# FEATURES & LABELS
# =========================
for each month t in 1980..2020:
    X_t := features available by end of t-1 (market, accounting (lagged), IBES, EDGAR text, macro, ratings)
    y_t := realized stock return over t+1..t+3 (DGTW-adjusted preferred)

# Preprocess within training folds only:
# - Winsorize features (type-specific rules)
# - Impute missing (numeric: quarter-mean; categorical/flags: 0)
# - Standardize numeric using train stats

# =========================
# ROLLING EXPANDING TRAINING
# =========================
for prediction year Y in 1986..2020:
    train_period := 1980-01 .. (Y-1)-10  # end in Oct Y-1 to avoid quarter overlap
    # time-series cross-validated randomized hyperparameter search (RF depth, trees, min split/leaf, mtry)
    fit RandomForest_Y on train_period to minimize validation MSE

    # =========================
    # PREDICT MONTHLY IN YEAR Y
    # =========================
    for each month t in Y:
        ŷ_t := RandomForest_Y.predict(X_t)
        # also compute within-DGTW ranks/deciles for portfolio rules

# Optionally also fit a Neural Network model; ensemble via average rank to get a small lift.

What Drives Predictions?

Permutation importance analysis shows simple features are highly influential:

• Market value, dollar volume, trading activity, earnings-forecast signals.
  
• RF captures nonlinear interactions among simple predictors.

Portfolio Construction – Shared Constraints

• No shorting; quarterly rebalance only.
  
• Within-style swaps: replacements must come from the same DGTW group.
  
• Depth/liquidity: cap any single holding to ≤ 20% of the stock’s market cap (clip and keep overflow).
  
• No duplicate replacements (“without replacement” within a fund/quarter).
  
• Payout convention: AI’s incremental gain is paid out quarterly so human and AI start next quarter with equal AUM (conservative for AI in dollars).

AI-Modified (Hybrid) – Pseudocode

inputs:
  w_h[j]      # human start-of-quarter weight for stock j
  g[j]        # DGTW group of stock j
  decile[j]   # predicted decile within g[j] (1=worst ... 10=best)
  ŷ[j]        # predicted DGTW-adjusted return
  NAV         # fund net asset value at start of quarter

initialize:
  w_ai := w_h
  used := ∅    # prevent duplicate use of replacement names

# Keep strong human picks
for j in holdings sorted by descending w_h[j]:
    if decile[j] == 10:
        used.add(j)

# Attempt upgrades for others (largest positions first)
for j in holdings sorted by descending w_h[j]:
    if decile[j] in 1..9:
        group := g[j]
        C := { s in group | decile[s] == 10 and s ∉ used }
        if C ≠ ∅:
            # choose best candidate
            k := argmax_s∈C ŷ[s]
            target_value := w_h[j] * NAV
            max_value := 0.20 * market_cap(k)
            delta_value := min(target_value, max_value)
            w_ai[k] +=  delta_value / NAV
            w_ai[j] -=  delta_value / NAV
            used.add(k)

# Replace remaining bottom-decile names with the group index
for j in holdings:
    if decile[j] == 1 and w_ai[j] > 0:
        idx := index_for_group(g[j])
        w_ai[idx] += w_ai[j]
        w_ai[j]   = 0

# Normalize / clean
project w_ai onto the simplex (weights ≥ 0, sum = 1)

AI-Only (Full Replacement) – Pseudocode

inputs as above
initialize:
  w_ai := 0
  used := ∅
  backlog[group] := 0 for all groups

# Map each human slot to a top-decile name in the same group
for j in human holdings sorted by descending w_h[j]:
    group := g[j]
    C := { s in group | decile[s] == 10 and s ∉ used }
    if C ≠ ∅:
        k := argmax_s∈C ŷ[s]
        target_value := w_h[j] * NAV
        max_value := 0.20 * market_cap(k)
        delta_value := min(target_value, max_value)
        w_ai[k] += delta_value / NAV
        used.add(k)
        # any leftover because of cap stays to be assigned:
        if delta_value < target_value:
            backlog[group] += (target_value - delta_value) / NAV
    else:
        backlog[group] += w_h[j]

# Push any leftover weight to the group index
for each group:
    if backlog[group] > 0:
        idx := index_for_group(group)
        w_ai[idx] += backlog[group]

project w_ai onto the simplex

Performance Measurement – Dollar Alpha

Let Rᵐᵢ,𝑞 be fund i’s gross return from observed holdings in quarter q.
Let Rᵇᵢ,𝑞 be the corresponding DGTW benchmark return (same weights, matched groups).

Dollar alpha (human):

Vᵢ,𝑞 = Assetsᵢ,𝑞−1 (Rᵐᵢ,𝑞 − Rᵇᵢ,𝑞)

Incremental dollars (AI over human):

Zᵢ,𝑞 = Assetsᵢ,𝑞−1 (Rᴬᴵᵢ,𝑞 − Rᵐᵢ,𝑞)

Aggregate to lifetime averages per fund, then time-weighted across funds.

Sharpe Ratio (Definition & Use)

For fund i with quarterly excess returns ERᵢ,𝑡 = Rᵢ,𝑡 − Rʳᶠₜ:

Sharpeᵢ = ( mean(ERᵢ) / σ(ERᵢ,𝑡) ) × √16

Compare paired Sharpe differences:

ΔSharpeᵢ = Sharpeᵢᴬᴵ − Sharpeᵢᴴᵘᵐᵃⁿ

Findings:

• Avg human Sharpe ≈ 0.47.
  
• Avg paired difference (AI-modified − human) ≈ +0.17 (t ≈ 69).
  
• ~95% of funds show a positive Sharpe improvement.
  
• Similar uplifts for AI-only.

Risk Adjustments & Robustness

• Factor alphas: FF5 + momentum, and with mispricing factors → AI outperformance persists or widens.
  
• Sharpe and CDF dominance: AI nearly first-order stochastically dominates human quarterly performance.
  
• Transaction costs:
  • Implied quarterly turnover: Human ~20%; AI-modified ~52% stocks + 3% indices; AI-only ~40% stocks + 10% indices.
    
  • Institutional cost estimates (≈13–37 bps per stock trade) → AI still dominates net of costs.
    
• Benchmarks: Results hold when restricting to funds with verified size/value benchmarks and style-consistent holdings.
  
• Incentives: Results hold for direct-sold (sophisticated) funds and for funds flagged as quantitative.

Why Human + Machine?

• Public-signal extraction is a skill; AI scales nonlinearity & interactions across simple signals.
  
• Constrained, style-consistent AI can deliver practical outperformance (not just paper alpha).

Hybrid process:

• Humans: mandate, domain context, governance, risk/compliance, private info where valuable.
  
• Machines: breadth, speed, nonlinearity, consistent execution, monitoring, “what-if”s.

Implementation Tips (Practitioner Slide)

• Data ops: point-in-time joins; strict lags; feature health checks; backtest hygiene (no leakage).
  
• Modeling: rolling expanding windows; time-series CV; monitor drift; ensemble RF/NN ranks.
  
• PM integration: within-style candidate pools; depth caps; turnover budgets; quarterly (or monthly) cadence; explicit payout/compounding policy.
  
• Risk: side-by-side factor loads; pre/post-trade limits; stress; transaction-cost controls.

Limitations & Scope

• Results are partial-equilibrium (single fund adopting AI). Widespread adoption → greater price impact, lower marginal gains.
  
• Lower-bound cost estimate: conservative sizing; quarterly payout prevents compounding of AI gains; RF today < RF+NN tomorrow.
  
• Private information could still add value; study quantifies public-info processing costs.

Takeaways

• Managers left economically large returns on the table by not further processing public data.
  
• Human + machine collaboration substantially improves risk-adjusted performance under real constraints.
  
• Challenges the idea that public info is “free” to use; processing costs are material.
  
• As AI improves, the shadow price of public information likely rises.